Cartesian Product Of Two Modular Fuzzy Metric Spaces

Authors

  • Mohammed Jawad مديرية تربية ذي قار

DOI:

https://doi.org/10.32792/jeps.v16i1.828

Abstract

This paper investigates the properties of modular fuzzy metric spaces and their Cartesian products.

 We begin with the basic definitions and properties of modular metrics, and modular fuzzy metrics.

The main results focus on establishing that the Cartesian product of two modular fuzzyk metric rspacesu isf itself  modular fuzzyt metricq space. We prove that convergence and Cauchy sequences in the product space correspond to the sequences in the component spaces. Furthermore, the completeness property is preserved under Cartesian products. These results provide a rigorous framework for further studies in fuzzy analysis and its applications in metric-based uncertainty modeling.

 

 

 

References

J. Buckley and E. Eslami, An introduction to fuzzy logic and fuzzy sets. New York: Physica-Verlag, 2002. doi: 10.1007/978-3-7908-1799-7.

N. U. Bostan and B. P. Varol, “On the structure of modular fuzzy metric space,” in Proc. 6th Int. Conf. Life and Engineering Sciences (ICOLES), Antalya, Turkey, 2023.

V. Chistyakov, “Modular metric spaces I: Basic concepts,” Nonlinear Anal., vol. 72, pp. 1–14, 2010. doi: 10.1016/j.na.2009.04.057.

V. Chistyakov, “Modular metric spaces II: Application to superposition operators,” Nonlinear Anal., vol. 72, pp. 15–30, 2010. doi: 10.1016/j.na.2009.04.018.

A.George and P.Veeramani,On some results in fuzzy metric spaces, fuzzy sets and systems

,,385-389,27-1988. https://doi.org/10.1016/0165-0114(94)90162-7

A. Muraliraj, P. Shanmugavel, and R. Thangathamizh, “Fixed point theorems on modular revised fuzzy metric spaces,” Commun. Appl. Nonlinear Anal., vol. 31, no. 3s, 2024. https://doi.org/10.52783/cana.v31.760

H. Nakano, Modular semi-ordered spaces. Tokyo, Japan: Maruzen, 1950.

F. N. Al-Mayahi and S. Al-ham Nief, “Some properties of Cartesian product of two fuzzy modular spaces,” Eng. Technol. J., vol. 6, no. 5, pp. 9279–9281, May 2019.

I. Kramosil and J. Michalek, “Fuzzy metric and statistical metric spaces,” Kybernetika, vol. 11, pp. 336–344, 1975. http://eudml.org/doc/28711

H. Kerim, W. Shatanawi, A. Tallafha, and T. A. M. Shatnawi, “Fixed points theorems on modular fuzzy metric spaces,” U.P.B. Sci. Bull., Ser. A, vol. 84, no. 1, 2022. https://doi.org/10.52783/cana.v31.760

B. Schweizer and A. Sklar, “Statistical metric spaces,” Pacific J. Math., vol. 10, pp. 313–334, 1960. doi: 10.2140/pjm.1960.10.313.

L.A.Zadeh,Fuzzy sets,Information and Control,338-353,8,1965. ∶ doi.org/10.2307/2272014

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Published

2026-03-01

Issue

Vol. 16 No. 1 (2026): JOURNAL OF EDUCATION FOR PURE SCIENCE

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